Predictive analysis of plankton population dynamics in marine biosphere: a nonlinear ARX neural network for the...

Plankton dynamics lie at the core of biogeochemical cycles and ecosystem function, which makes dependable prediction essential. Neural network-based approximations show strong potential in capturing these nonlinear interactions due to their flexibility and efficiency. In this study, a dynamic nonlinear autoregressive exogenous neural network trained with the Levenberg-Marquardt algorithm (ARX-LMA) is exploited on the nonlinear carbon thermal nutrient-plankton autonomous dynamics (NCTNP-AD) system for plankton population in the marine biosphere influenced by the impact of global warming and climate change. Four nonlinear ordinary differential equations construct the asymmetric multifactor NCTNP-AD system reflected by the concentrations of carbon dioxide, temperature, nutrient, and plankton population in the marine biosphere. The Adams numerical solver is efficiently utilized to create synthetic temporals by varying rates of plankton maintaining the CO₂ concentration by assimilating dissolved nutrients via membrane transporters in response to temperature, the net carbon dioxide absorption rate by the plankton population density, and the predation rate of plankton by fish within the NCTNP-AD system essentially fueling marine primary production. The neuro-computing-based ARX-LMA networks are specifically trained on these datasets to quantify, model, and anticipate the population density changes of the plankton community via a multifactor asymmetric NCTNP-AD system under global warming conditions. The novel ARX-LMA technique's efficacy is thoroughly validated across simulated reference solutions. The comparison includes error convergence graphs, training response graphs, hyperparameter state graphs, error-input correlations, error autocorrelation, regression analysis, error histograms, absolute error, and corresponding reconstruction graphs. Single- and multi-step ahead ARX-LMA predictors were expertly constructed to predict the effects of global warming on plankton population. Step-ahead and multi-step prediction errors in the range of 10^-10 to 10^-12 affirm the efficacy of ARX-LMA in accurately modeling and forecasting the complex NCTNP-AD system. These findings showcase that machine-learning-based surrogates can provide accurate and adaptable emulators and forecasters of coupled plankton dynamics.